How to use pyxtal - 10 common examples

position, and makes sure at least one valid combination of WP's exists.
        """
        # Store whether or not at least one degree of freedom exists
        has_freedom = False
        # Store the wp's already used that don't have any freedom
        used_indices = []
        # Loop over species
        for i_mol, numIon in enumerate(numMols):
            # Get lists of multiplicity, maxn and freedom
            l_mult0 = []
            l_maxn0 = []
            l_free0 = []
            indices0 = []
            for i_wp, wp in enumerate(group):
                # Check that at least one valid orientation exists
                j, k = jk_from_i(i_wp, group.wyckoffs_organized)
                if len(valid_orientations[i_mol][j][k]) > 0:
                    indices0.append(i_wp)
                    l_mult0.append(len(wp))
                    l_maxn0.append(numIon // len(wp))
                    if np.allclose(wp[0].rotation_matrix, np.zeros([3, 3])):
                        l_free0.append(False)
                    else:
                        l_free0.append(True)
            # Remove redundant multiplicities:
            l_mult = []
            l_maxn = []
            l_free = []
            indices = []
            for mult, maxn, free, i_wp in zip(l_mult0, l_maxn0, l_free0, indices0):
                if free is True:
                    if mult not in l_mult:

try:
        import pyxtal.symmetry
    except Exception as e:
        fail(e)

    print("  get_wyckoffs (may take a moment)")
    try:
        from pyxtal.symmetry import get_wyckoffs
    except Exception as e:
        fail(e)

    if passed():
        try:
            for i in [1, 2, 229, 230]:
                get_wyckoffs(i)
                get_wyckoffs(i, organized=True)
        except:
            fail(" Could not access Wyckoff positions for space group # " + str(i))

    check()

    print("  get_wyckoff_symmetry (may take a moment)")
    try:
        from pyxtal.symmetry import get_wyckoff_symmetry
    except Exception as e:
        fail(e)

    if passed():
        try:
            for i in [1, 2, 229, 230]:
                get_wyckoff_symmetry(i)
                get_wyckoff_symmetry(i, molecular=True)

else:
            lattice = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
            old_coords = np.array(crystal)
            old_species = ["C"] * len(old_coords)

        from pyxtal.symmetry import distance
        from pyxtal.symmetry import filtered_coords
        from copy import deepcopy

        PBC = [1, 1, 1]

        # Obtain the generators for the group
        if dim == 3:
            from pyxtal.symmetry import get_wyckoffs

            generators = get_wyckoffs(group)[0]

        elif dim == 2:
            from pyxtal.symmetry import get_layer

            generators = get_layer(group)[0]
            PBC = [1, 1, 0]
        elif dim == 1:
            from pyxtal.symmetry import get_rod

            generators = get_rod(group)[0]
            PBC = [0, 0, 1]
        elif dim == 0:
            from pyxtal.symmetry import Group

            generators = Group(group, dim=0)[0]
            PBC = [0, 0, 0]

except Exception as e:
            fail(e)

    check()

    print("  ss_string_from_ops")
    try:
        from pyxtal.symmetry import ss_string_from_ops
    except Exception as e:
        fail(e)

    if passed():
        try:
            strings = ["1", "4 . .", "2 3 ."]
            for i, sg in enumerate([1, 75, 195]):
                ops = get_wyckoffs(sg)[0]
                ss_string_from_ops(ops, sg, dim=3)
        except Exception as e:
            fail(e)

    check()

    print("  Wyckoff_position")
    try:
        from pyxtal.symmetry import Wyckoff_position
    except Exception as e:
        fail(e)

    if passed():
        try:
            wp = Wyckoff_position.from_group_and_index(20, 1)
        except Exception as e:

reset()
    try:
        import pyxtal.symmetry
    except Exception as e:
        fail(e)

    print("  get_wyckoffs (may take a moment)")
    try:
        from pyxtal.symmetry import get_wyckoffs
    except Exception as e:
        fail(e)

    if passed():
        try:
            for i in [1, 2, 229, 230]:
                get_wyckoffs(i)
                get_wyckoffs(i, organized=True)
        except:
            fail(" Could not access Wyckoff positions for space group # " + str(i))

    check()

    print("  get_wyckoff_symmetry (may take a moment)")
    try:
        from pyxtal.symmetry import get_wyckoff_symmetry
    except Exception as e:
        fail(e)

    if passed():
        try:
            for i in [1, 2, 229, 230]:
                get_wyckoff_symmetry(i)

from time import time
    from spglib import get_symmetry_dataset
    from pyxtal.symmetry import get_wyckoffs
    from pyxtal.crystal import random_crystal
    from pyxtal.crystal import cellsize
    from pymatgen.symmetry.analyzer import SpacegroupAnalyzer

    slow = []
    failed = []
    print("  Spacegroup #  |Generated (SPG)|Generated (PMG)|  Time Elapsed")
    skip = (
        []
    )  # [124, 139, 166, 167, 196, 202, 203, 204, 207, 209, 210, 216, 217, 219, 220, 221, 223, 225, 226, 227, 228, 229, 230] #slow to generate
    for sg in range(1, 231):
        if sg not in skip:
            multiplicity = len(get_wyckoffs(sg)[0]) / cellsize(
                sg
            )  # multiplicity of the general position
            start = time()
            rand_crystal = random_crystal(sg, ["C"], [multiplicity], 1.0)
            end = time()
            timespent = np.around((end - start), decimals=2)
            t = str(timespent)
            if len(t) == 3:
                t += "0"
            t += " s"
            if timespent >= 1.0:
                t += " ~"
            if timespent >= 3.0:
                t += "~"
            if timespent >= 10.0:
                t += "~"

else:
                fail()
        except Exception as e:
            fail(e)

    check()

    print("  index_from_letter")
    try:
        from pyxtal.symmetry import index_from_letter
    except Exception as e:
        fail(e)

    if passed():
        try:
            if index_from_letter("A", get_wyckoffs(47)) == 0:
                pass
            else:
                fail()
        except Exception as e:
            fail(e)

    check()

    print("  jk_from_i")
    try:
        from pyxtal.symmetry import jk_from_i
    except Exception as e:
        fail(e)

    if passed():
        try:

def compare_wyckoffs(num1, num2, dim=3):
    """Given 2 groups, return whether the second point
    group has equal or greater symmetry than the first group."""
    from numpy import allclose

    if num1 == "???":
        print("Error: invalid value for num1 passed to compare_wyckoffs")
        return
    if num2 == "???":
        return False
    # Get general positions for both groups
    if dim == 3:
        from pyxtal.symmetry import get_wyckoffs

        g1 = get_wyckoffs(num1)[0]
        g2 = get_wyckoffs(num2)[0]
    elif dim == 2:
        from pyxtal.symmetry import get_layer

        g1 = get_layer(num1)[0]
        g2 = get_layer(num2)[0]
    elif dim == 1:
        from pyxtal.symmetry import get_rod

        g1 = get_rod(num1)[0]
        g2 = get_rod(num2)[0]
    elif dim == 0:
        from pyxtal.symmetry import get_point

        g1 = get_point(num1)[0]
        g2 = get_point(num2)[0]
    # If group 2 has higher symmetry

def compare_wyckoffs(num1, num2, dim=3):
    """Given 2 groups, return whether the second point
    group has equal or greater symmetry than the first group."""
    from numpy import allclose

    if num1 == "???":
        print("Error: invalid value for num1 passed to compare_wyckoffs")
        return
    if num2 == "???":
        return False
    # Get general positions for both groups
    if dim == 3:
        from pyxtal.symmetry import get_wyckoffs

        g1 = get_wyckoffs(num1)[0]
        g2 = get_wyckoffs(num2)[0]
    elif dim == 2:
        from pyxtal.symmetry import get_layer

        g1 = get_layer(num1)[0]
        g2 = get_layer(num2)[0]
    elif dim == 1:
        from pyxtal.symmetry import get_rod

        g1 = get_rod(num1)[0]
        g2 = get_rod(num2)[0]
    elif dim == 0:
        from pyxtal.symmetry import get_point

        g1 = get_point(num1)[0]
        g2 = get_point(num2)[0]

for i in [1, 2, 229, 230]:
                get_wyckoff_generators(i)
        except:
            fail("Could not access Wyckoff generators for space group # " + str(i))

    check()

    print("  letter_from_index")
    try:
        from pyxtal.symmetry import letter_from_index
    except Exception as e:
        fail(e)

    if passed():
        try:
            if letter_from_index(0, get_wyckoffs(47)) == "A":
                pass
            else:
                fail()
        except Exception as e:
            fail(e)

    check()

    print("  index_from_letter")
    try:
        from pyxtal.symmetry import index_from_letter
    except Exception as e:
        fail(e)

    if passed():
        try: